Partial Derivative of Second Order Problem 4

TL;DR

This video explains how to find the value of second order partial differentiation using the example of a given function.

Transcript

hi students so after covering the third problem on the partial differential of second order let's move to the next problem so here we have a different question to solve and obviously the function will be different so let's see how to get its value by finding the partial differentiation of second order so the value of u is given as f of r square whe... Read More

Key Insights

• 🎮 The video explains the process of finding the value of second order partial differentiation.
• 🛟 The function u = f(r^2) serves as an example to demonstrate the calculation.
• 🤪 Differentiating the function twice with respect to x, y, and z provides the necessary values for partial differentiation.
• 🥺 Substituting the given values and simplifying the equations leads to the final result matching the given result.
• 🎮 The video emphasizes the importance of understanding second order partial differentiation for engineering subjects.
• ❓ The concept can be applied to various problems and equations related to partial differentiation.
• 🎮 The video promotes the eKeda channel as a reliable source for engineering subjects under one roof.

Questions & Answers

Q: What is the function given in the video for finding the second order partial differentiation?

The function given in the video is u = f(r^2), where r^2 = x^2 + y^2 + z^2.

Q: How does the video explain the process of finding the partial differentiation values?

The video explains the process by differentiating the function with respect to x, y, and z separately, and then simplifying the equations.

Q: What are the values of the partial differentiation obtained in the video?

The values obtained for the partial differentiation are: del square u/del x square = 4x^2f''(r^2) + 6f'(r^2), del square u/del y square = 4y^2f''(r^2) + 6f'(r^2), and del square u/del z square = 4z^2f''(r^2) + 6f'(r^2).

Q: How does the final result match the given result in the video?

By substituting r^2 = x^2 + y^2 + z^2 into the equations and simplifying, the final result obtained matches the given result.

Summary & Key Takeaways

• The video discusses how to calculate the value of second order partial differentiation for a given function.

• The function in question is u = f(r^2), where r^2 = x^2 + y^2 + z^2.

• By differentiating the function with respect to x, y, and z twice, the partial differentiation values are obtained.

• Through simplification and substituting the given values, the final result matches the given result.